Estimation of Nonlinear Viscoelastic Parameters from Estimated Linear Models of Behavior around Multiple Settling Points of a Foam-Mass System

Yousof Azizi; Vaidyanadan Sundaram; Patricia Davies; Anil Bajaj

doi:10.4271/2014-01-0851

Unveiling Temporal Nonlinear Structure–Rheology Relationships under Dynamic Shearing

Polymers ◽

10.3390/polym11071189 ◽

2019 ◽

Vol 11 (7) ◽

pp. 1189 ◽

Cited By ~ 8

Author(s):

Johnny Ching-Wei Lee ◽

Lionel Porcar ◽

Simon A. Rogers

Keyword(s):

3D Structure ◽

Uniaxial Extension ◽

Soft Materials ◽

Equilibrium Structure ◽

Nonlinear Structure ◽

Natural Approach ◽

Viscoelastic Parameters ◽

3D Space ◽

Nonlinear Viscoelastic ◽

Dynamic Shearing

Understanding how microscopic rearrangements manifest in macroscopic flow responses is one of the central goals of nonlinear rheological studies. Using the sequence-of-physical-processes framework, we present a natural 3D structure–rheology space that temporally correlates the structural and nonlinear viscoelastic parameters. Exploiting the rheo-small-angle neutron scattering (rheo-SANS) techniques, we demonstrate the use of the framework with a model system of polymer-like micelles (PLMs), where we unveil a sequence of microscopic events that micelles experience under dynamic shearing across a range of frequencies. The least-aligned state of the PLMs is observed to migrate from the total strain extreme toward zero strain with increasing frequency. Our proposed 3D space is generic, and can be equally applied to other soft materials under any sort of deformation, such as startup shear or uniaxial extension. This work therefore provides a natural approach for researchers to study complex out-of-equilibrium structure–rheology relationships of soft materials.

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A nonlinear viscoelastic model of lung tissue mechanics

Journal of Applied Physiology ◽

10.1152/jappl.1991.71.3.826 ◽

1991 ◽

Vol 71 (3) ◽

pp. 826-833 ◽

Cited By ~ 60

Author(s):

B. Suki ◽

J. H. Bates

Keyword(s):

Lung Tissue ◽

Linear Models ◽

Viscoelastic Model ◽

Low Frequency ◽

Simulated Data ◽

Tissue Mechanics ◽

Model Parameters ◽

Volume Dependence ◽

Nonlinear Viscoelastic ◽

Nonlinear Viscoelastic Model

There have been a number of attempts recently to use linear models to describe the low-frequency (0–2 Hz) dependence of lung tissue resistance (Rti) and elastance (Eti). Only a few attempts, however, have been made to account for the volume dependence of these quantities, all of which require the tissues to be plastoelastic. In this paper we specifically avoid invoking plastoelasticity and develop a nonlinear viscoelastic model that is also capable of accounting for the nonlinear and frequency-dependent features of lung tissue mechanics. The model parameters were identified by fitting the model to data obtained in a previous study from dogs during sinusoidal ventilation. The model was then used to simulate pressure and flow data by use of various types of ventilation patterns similar to those that have been employed experimentally. Rti and Eti were estimated from the simulated data by use of four different estimation techniques commonly applied in respiratory mechanics studies. We found that the estimated volume dependence of Rti and Eti is sensitive to both the ventilation pattern and the estimation technique, being in error by as much as 217 and 22%, respectively.

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Nonlinear viscoelastic oscillations of single-mass system at power excitation

E3S Web of Conferences ◽

10.1051/e3sconf/202128402010 ◽

2021 ◽

Vol 284 ◽

pp. 02010

Author(s):

Nurilla Noraliev ◽

Fatimat Kudaeva ◽

Karamatilla Khayitboev ◽

Zokhid Kusharov ◽

Abrorjon Turgunov ◽

...

Keyword(s):

Computer Program ◽

Rheological Properties ◽

Solution Method ◽

Nonlinear Oscillations ◽

Quadrature Formulas ◽

Mass System ◽

Nonlinear Viscoelastic ◽

Fixed Base ◽

Single Mass ◽

Force Excitation

Nonlinear oscillations of single-mass system at force excitation of vibration connected with fixed base by weightless viscoelastic spring are considered. To take into account the rheological properties of the spring material, the Boltzmann-Volterr principle was used. Mathematical models of the problem in question are obtained, which are described by nonlinear integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis, the results of which are reflected in the form of graphs. Influence of nonlinear and rheological properties of spring on amplitude and phase of mass oscillations is investigated.

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The Normal Impact of an Elastic Rod-Mass System on a Viscoelastic Half Space

Journal of Applied Mechanics ◽

10.1115/1.3173021 ◽

1987 ◽

Vol 54 (2) ◽

pp. 367-372

Author(s):

H. A. Downey ◽

D. B. Bogy

Keyword(s):

Integral Equation ◽

Half Space ◽

Elastic Rod ◽

Lumped Mass ◽

Normal Impact ◽

Mass System ◽

Viscoelastic Parameters ◽

Large Hysteresis ◽

Viscoelastic Effects ◽

The Impact

The normal impact of a one-dimensional elastic rod, with a lumped mass on the trailing end, onto a viscoelastic half space is considered and the problem is solved for the time dependent interface stress and displacement. The problem is reduced to an integral equation, whose two-part kernel consists of solutions of two simpler problems. One part pertains to the half space only and the other is for the rod-mass system. The half-space portion of the kernel is obtained through a numerical inversion of the Laplace transformed solution. Given the half-space kernel contribution, which depends only on the two viscoelastic parameters and Poisson’s ratio, the integral equation is solved numerically for two families of half space materials. The viscoelastic effects on the half space are quite pronounced. Certain combinations of the parameters cause a large hysteresis in the impact, and softer half spaces require longer contact times before the rod leaves the surface.

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Characterizing Damping and Restitution in Compliant Impacts via Linear Viscoelastic Models

Volume 7B: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8335 ◽

1999 ◽

Author(s):

Eric A. Butcher ◽

Daniel J. Segalman

Keyword(s):

Linear Models ◽

Energy Losses ◽

Displacement Boundary ◽

Viscoelastic Models ◽

Viscoelastic Parameters ◽

Linear Viscoelastic ◽

Standard Linear ◽

Linear Damping ◽

Voigt Model ◽

Force Displacement

Abstract Strategies for characterizing damping and restitution in compliant impacts while eliminating the force discontinuities associated with the standard Kelvin-Voigt model are examined within the framework of linear viscoelasticity. A modification of the Kelvin-Voigt model as well as higher-order (Maxwell and standard linear) models are studied in an effort to satisfy the expected force-displacement boundary conditions. The restitution coefficients, energy losses per cycle, and equivalent linear damping ratios are then obtained analytically as functions of the dimensionless viscoelastic parameters which may be easily related to and obtained from experimentally measured restitution coefficients.

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Shock Wave as a Mechanism of Injury in Soft Tissues

ASME 2011 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2011-53823 ◽

2011 ◽

Author(s):

Kaveh Laksari ◽

Kurosh Darvish ◽

Keyanoush Sadeghipour

Keyword(s):

Soft Tissues ◽

Linear Models ◽

Initial Conditions ◽

Soft Tissue Injuries ◽

High Rate ◽

Loading Conditions ◽

Mechanism Of Injury ◽

Nonlinear Viscoelastic ◽

Nonlinear Viscoelastic Materials ◽

High Rate Loading

The aim of this study is to investigate the propagation of shock waves and self-preserving waves in soft tissues such as aorta and brain as a mechanism of injury in high rate loading conditions as seen in blunt trauma and blast-induced trauma (BIT). It is shown that such phenomena can only be seen in nonlinear viscoelastic materials and the existing linear and quasi-linear models predict only decaying waves. Based on the results of this study, it is shown that when studying such high-rate loading conditions as in a blast, it is critical to consider the discontinuities predicted in strain and stress in certain realistic initial conditions to accurately determine the extent of soft tissue injuries.

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